knjiga solarna energija dobra

106 THE PHYSICS OF THE SOLAR CELL
The open-circuit current expression, equation (3.140), can be rearranged and the
temperature dependence explicitly included to give
I SC ≈ I o1 e qV OC/kT ≈ BT ζ e −E G(0)/kT e qV OC/kT
(3.159)
where B is a temperature-independent constant and T ζ e −E G(0)/kT accounts for the temperature
dependence of the saturation current. The short-circuit current is relatively unaffected
by temperature under typical operating conditions, so by differentiating with respect to
T , the temperature dependence of the open-circuit voltage can be expressed as [15]
1
dV OC
dT =− q E G(0) − V OC + ζ kT q
T
(3.160)
which for silicon at 300 K corresponds to about −2.3 mV/ ◦ C. Equation (3.159) can be
rearranged as follows:
V OC (T ) = 1 q E G(0) − kT q ln ( BT
ζ
I SC
)
. (3.161)
V OC varies roughly linearly and inversely with temperature and an extrapolation of V OC
to T = 0 is approximately the band gap since lim T →0 [T ln T ] = 0.
3.5.5 Concentrator Solar Cells
Operating solar cells under concentrated illumination offers two main advantages. The first
is that since fewer solar cells are required to collect the sunlight falling on a given area,
their cost of manufacture can be higher than that for cells designed for nonconcentrated
illumination, and they are therefore presumably of higher quality (efficiency). The second
is that operation under concentrated illumination offers an advantage in the solar cell
efficiency. If sunlight is concentrated by a factor of X (X sun illumination), the short
circuit at that concentration is
I Xsuns
SC
= XI 1sun
SC . (3.162)
This is assuming that the semiconductor parameters are unaffected by the illumination
level and that the cell temperature is the same at both levels of illumination – not necessarily
valid assumptions especially at very large X, that is, X > 100. However, these
assumptions will allow the demonstration of the potential efficiency of concentrator solar
cells. Substituting equation (3.162) into equation (3.135) gives
η = FFXsuns VOC
Xsuns ISC
Xsuns
Pin
Xsuns
= FFXsuns VOC
Xsuns XISC
1sun
XPin
1sun
= FFXsuns VOC
Xsuns ISC
1sun
Pin
1sun
(3.163)
From equation (3.131),
V Xsuns
OC
= V 1suns
OC + kT q
ln X. (3.164)